Common Distance Metrics Implemented in Ruby

The starting point for many machine learning tasks is to describe your entities in terms of a set of features. For example, in text-based learning your features might be the frequency of different words, or for an image-based task your starting features could be pixel intensity values. Typically we attempt to represent our entities as an array of numerical elements, amenable to machine learning algorithms.When represented in this format it is often useful to consider which entities are 'close together'. This concept of proximity is important for clustering algorithms, nearest-neighbour algorithms, generating recommendations and much more. But how do we calculate the distance between two vectors?.